Uniform one-factorisations of the complete bipartite graph

Last modified: Sept. 5, 1996

Joint work with Gillian Nonay with significant contributions from Dan Archdeacon and Gordon Royle. Thanks to Cindy Lau for help in setting up these Web pages.

These pages are still under construction. In particular, the table is incomplete; some known examples remain to be entered.

Select items from the table at left.


The table at left lists, for 2<=n<=11, all possible partitions of the integer n into parts of size larger than one. For example, the partition of 8 into 3+3+2 is encoded as [3,3,2]. For each such partition [k1,k2, ...,ks], we ask "Is there a one-factorisation of the complete bipartite graph Kn,n having the property that the union of any two distinct one-factors is isomorphic to a 2-regular graph having components of size 2k1, 2k2,..., 2k1?" The table indicates "Yes" if an example is known, "No" if it is known that no example exists, and "?" in the remaining cases. If one clicks on any link in the table, an example, construction, or non-existence argument appears in the frame above.